查询词典 theorem

We have obtained the dual cross product 〓 if a Kac-systemacts on a Hilbert 〓-module E;then we generalized Baaj and Skandalis'duality theorem.

我们得到当一Kac-系统作用在〓模E上时，两次交叉积E×S×S等价于〓；从而，Baaj和Skandalis的对偶理论是我们的一个特殊形式。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

In this paper, the nonexistence of the closed orbit which circles the equilibrium is proved by using the Dulac function, then all the orbits of the system are bounded by the Filippov transformation and comparability theorem.

本文利用Dulac函数法，首先判定了不存在绕平衡点的闭轨线，然后利用Filippov变换和比较定理，证明了系统所有轨线的有界性，进而得到了平衡点是全局渐近稳定的。

Based on this relation, it is possible not only to obtain the principle of virtual work and the reciprocal theorem in dyn...

然后从该式出发，不仅可以得到有孔隙的耦合热弹性体动力学的虚功原理和互等定理，而且能系统地导出成互补关系的11类变量、9类交量、6类变量及3类变量简化Gurtin型变分原理。

By use of residue theorem,the trace identity of eigenvalue which correspond to the eigenvalue problem is obtained.

讨论了一个带非局部项的微分方程初值问题解的渐进估计，并利用留数定理给出相应特征值问题特征值的迹公式。

This solution has no relation with properties of the imaginary isotropic layer, and this is consistent with the uniqueness theorem of elastodynamics.

所得结果和假想层的力学性质无关，符合弹性力学问题的唯一性定理。

This theorem has curious properties and important applications, but still not appreciated quite well in the present paper of electrostatics of China.

该定理在精确计量学上具有重要的用途，然而国内相关领域文献很少涉及。

In this paper,using the elementary row operation on a matrix theorem,we present two methods for solving the eigenvalues and the eigenvectors.

利用矩阵的初等变换理论，详细讨论了两种特征值和特征向量的求法

Chapter 1 mainly introduce some elementary concepts about matrix: consistently ordered matrix, matrix norm, nonnegative matrix and famous Perron-Frobenius theorem.

介绍了矩阵的一些基本概念：相容次序矩阵、矩阵范数、非负矩阵及著名的Perron-Frobenius定理等。

By using the Groebner bases theory and elimination theorem, we constructed a new algorithm of the algebraic attacks on nonlinear combiners with memory based on the previous works, and also analyzed its computation complexity in detail.

在已有工作的基础上，利用Groebner基理论及消元定理，构造了一种新的对带记忆非线性组合生成器的代数攻击算法，并对算法的计算复杂度进行了分析。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新